After you complete 4 world quests of the faction you see on your map, you can go to the emissary and claim your reward.You will always get 1 reputation Insignia like Fregio Superiore della Tribù Alto Monte. The list is at the bottom of this post.Kirin Tor daily gives you any reputation Insignia you want to. Can choose reward yourself

You have 3 daily quest and you have 3 days to complete it.1 quest changes every daySo it feels like daily, but you can just wait 2 days and then complete all 3 quests.No need to do them every day.They work similar to the dungeon or raid lockouts. Everyone have the same 3 quests.

I'll just list the quests and the emissary you should visit to claim the reward

Treasure chestsYou can get +250 reputation Insignia (like Fregio della Tribù Alto Monte) from lots of treasure chests in all 5 zones.The drop rate is extremely low, 5% or less, actually i got only 2 insignias after ~200 chestsThe full list of items you can get is at the bottom of the postYou can try to find more info here:

Order Hall missionsAt 110 level you will unlock missions in you garrison that reward you with another type of boa InsigniaLike this one Fregio della Tribù Alto Monte Full list is at the bottom of the postExtra reward is Tributo delle Isole Disperse and it is just 1 more reputation Insignia with random faction